Fletchling is the weakest user of ember, doing about 80-96% in scenario one and 0.3% in scenario two. Lets get into the details.
The first scenario is somewhat unclear, but we'll assume kartana has a jolly nature, the opposing Pokemon a timid one, and run standard sweeping sets of 252 Spa/Atk, 252 Spe, and 4 SpD with no item on either. Bagon and fletchling tie for the weakest ember user, and you can argue fletchling is weaker because bagon gets the ability sheer force. We'll use fletchling for our purposes. In the end we end up doing 80.3 - 95.7%. In the event both Pokemon were meant to be jolly, we get 72.5 - 86.4%. That's scenario one, but what about scenario two?
The first thing I did was set the EVs to make kartana extremely specially defensive with an EV spread of 252 HP, 4 Atk, 252 SpD, and make fletchling 0 Spa, the damage being 27.3 - 32.2%. The natures are the next step, giving kartana a calm nature and fletchling a jolly one. We end up doing 27.3 - 32.2%. Then we simply remove the IVs from fletchling next, giving us 16.1 - 19.8%. I next added light screen and rain on the field, and gave kartana an assault vest, doing 2.4 - 3.1%. Now lets finally adjust the levels, making fletchling level 1 and kartana level 100. This makes ember do 0.3 - 0.6%. Now stat changes will be added, making fletchling -6 special attack, and kartana +6 Special defense. The damage amount is still the same, 0.3 - 0.6%. The final change we will make before concluding is giving kartana a water tera type, doing 0.3%, always.
Source: The showdown damage calculator
Disclaimer: in the original post, it mentions that for scenario two, you can adjust stats, which I assume means stat changes like what cosmic power gives you, not actual base stats otherwise it would be more like blissey than kartana. I also put in regular rain instead of heavy rain, so ember would do some damage, and assumed we were in a single battle, not a double battle, so no friend guard. I will also mention water sport, but that isn't in the damage calculator settings, and 0.3% percent ends up being 1 damage, so it doesn't really matter too much.